for the following equation, state the value of the discriminant and then describe the nature of the solution 11x^2+4x+18=0
What is the value of the discriminant?
Which one is correct?
a. the equation has two real solutions
b. the equation has two imaginary solutions.
c. the equation has only one real solution
b^2-4ac = 16-big positive number 44*18
therefore equation has no real solutions
i want to learn algebra
To find the value of the discriminant, we need to use the formula for the discriminant, which is given by b^2 - 4ac. In this case, the equation is 11x^2 + 4x + 18 = 0.
Let's identify the values of a, b, and c from the equation:
a = 11,
b = 4,
c = 18.
Now, we can substitute these values into the discriminant formula:
Discriminant = b^2 - 4ac = (4^2) - 4(11)(18)
Calculating this expression:
Discriminant = 16 - 792 = -776
The value of the discriminant in this case is -776.
Now, let's determine the nature of the solution based on the value of the discriminant:
Since the discriminant is negative (-776), we can conclude that the equation has two imaginary solutions. Therefore, the correct answer is b. The equation has two imaginary solutions.